Access the full text.
Sign up today, get DeepDyve free for 14 days.
The minrank over a field F of a graph G on the vertex set 1,2, ,n is the minimum possible rank of a matrix M Fn n such that Mi, i 0 for every i, and Mi, j =0 for every distinct non-adjacent vertices i and j in G. For an integer n, a graph H, and a field F, let g(n,H, F) denote the maximum possible minrank over F of an n-vertex graph whose complement contains no copy of H. In this article, we study this quantity for various graphs H and fields F. For finite fields, we prove by a probabilistic argument a general lower bound on g(n,H,F), which yields a nearly tight bound of ( n/ log n) for the triangle H=K3. For the real field, we prove by an explicit construction that for every non-bipartite graph H, g(n,H, R) n for some = (H)> 0. As a by-product of this construction, we disprove a conjecture of Codenotti et al. [11]. The results are motivated by questions in information theory, circuit complexity, and geometry.
ACM Transactions on Computation Theory (TOCT) – Association for Computing Machinery
Published: May 7, 2019
Keywords: Minrank
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.